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<b>let </b><font color="Maroon">B</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">A</font>;<br/>

<b>thus </b><a NAME="E1:59_1_1"/>
( <font color="Maroon">B</font> is <a href="altcat_1.html#V9">semi-functional</a> &amp; <font color="Maroon">B</font> is <a href="yellow18.html#V3">set-id-inheriting</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow21.html#D4" target="_self">YELLOW21:def 4</a><br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">b</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="altcat_2.html#T30">ALTCAT_2:30</a></i>;<br/><a NAME="E2:59_1_1_1"/>
<font color="Maroon">a</font> is   <a href="waybel_0.html#NM8">LATTICE</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:59_1_1_1"/>
<font color="Maroon">b</font> is   <a href="waybel_0.html#NM8">LATTICE</a>
 ;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>, <font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>;<br/>

<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="altcat_2.html#T30">ALTCAT_2:30</a></i>;<br/>
<b>let </b><font color="Maroon">A</font> be   <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">B</font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><a NAME="E4:59_1_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/>

<a NAME="E5:59_1_1"/><b>then </b>
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a'</font>,<font color="Maroon">b'</font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a'</font>,<font color="Maroon">b'</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="orders_3.html#K1">MonFuncs</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> )
 
<b>by </b><i>, <a class="ref" href="altcat_2.html#T32">ALTCAT_2:32</a></i>;<br/>
<b>hence </b><a NAME="E6:59_1_1"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="orders_3.html#K1">MonFuncs</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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